Pardew guided Palace to last season's FA Cup final where they lost to Manchester United in extra time.
Pardew, 55, guided Palace to last season's FA Cup final where they lost to Manchester United in extra time but their Premier League form this term has been poor.
They have won just four of their 17 matches and only one of their last 11, and are presently only a point above the relegation places.
The immediate frontrunner to replace Pardew appeared to be Sam Allardyce, whose England reign lasted just one match before he had to resign after making ill-advised remarks to undercover reporters.
"I would like to put on record our sincere gratitude for the tremendous service Alan has given us, both in his time here as manager and previously as a player," said Parish in a statement published on the club website.
"Following a fantastic second half of 2014/15, the 2015/16 season culminated in only narrowly missing out on winning the FA Cup as well as securing our Premier League place for a record breaking fourth time."
Parish said Pardew, who played for the club as well and described his return when appointed manager in early 2015 as a homecoming, had left a legacy which would benefit Palace for years to come.
"During his tenure Alan's hard work and dedication were without question, he has improved so many areas of the club and we wish him the very best for the future," said Parish.
"With games now coming thick and fast over the holiday period the club are hoping to put someone in place as quickly as possible but have nothing to say about a replacement at this time."
Pardew, whose previous managerial jobs include West Ham United, Southampton and Newcastle United, said his "special bond" with the Eagles had not been affected by the ending of his managerial reign.
"I would just like to take the opportunity to thank everybody at Crystal Palace for their fantastic support," said Pardew.
"In particular a big thanks to the players who gave me absolutely everything and Steve Parish and his Board.
"Personally I have a lot of good feelings for this football Club and am sad that my time there has ended."